Mary Baker Eddy gives us a definition of "Church" in "Science and Health with Key to the Scriptures" (p. 583) which falls into two sections. The first section defines the absolute, spiritual Church, and reads as follows: "Church. The structure of Truth and Love; whatever rests upon and proceeds from divine Principle."
Considering this "structure of Truth and Love," we realize that God is Truth and Love, and that He is also Spirit and Mind. Therefore the structure of His creating must necessarily be spiritual, not material; mental, not physical. It is this concept of Church as a spiritual idea to which Christ Jesus referred in his conversation with Peter: he spoke of Peter as a rock, but in the symbolistic language of the era the rock must have stood for the truth of being which Peter had grasped when he said Matt. 16:16), "Thou art the Christ, the Son of the living God." And it was upon this rock, or divine idea, that Jesus intended founding his church.
In Peter's first epistle we encounter the same spiritual concept of church in his reference to the Christians as "lively stones" building up a spiritual house. Peter saw that the spiritual Church, the Church of God's creating, has always existed in full perfection, and that spiritual man is inseparable from it.